setting boundary condition for curvlinear grid
Dear fellows,
I am desperate for assistance please!! I converted my FV Cartesian code for incompressible (primitive variable) NavierStokes solver to a general boundary fitted curvilinear coordinate system, written in a strong conservative form, with the physical velocity being directly solved. I spend about 15 days on that and I am certain I did right on evaluating the metrics of the Jacobean (transformation matrix), the volume flux and pressure correction, etc. For instance I calculated the Jacobean as ja_i^j=\partial x_i/\partial \zeta_i; I find the area of the cell faces a_i^j=transpose(inverse(ja_i^j)). I bench marked the code for rectangular grid using Ghia82 driven cavity flow. It works ok up to this. Now I have some problem implementing Dirichlet boundary condition, trying to reproduce the skewed driven cavity problem. I assume U1=A11*u1+A21*u2, U2=A12*uf1+A22*uf2, etc. with Ui and ufi being the volume flux and physical velocities at the faces of the cells respectively. For start I evaluated the cell face velocities using centered averages from consecutive grids, ie uf1=0.5(u1_i+u1_i+1), etc. In many papers I came across, they don't discuss how to implement the bc, and I thought it is trivial. So I set u1=u2=0 at bottom , left and right faces of the cavity, u1=1, v1=0 at the top face. But the result I got is different with Demirdzic92. I exhausted all avenues to find where I went wrong, with no avail. By the way I used CDS and 2nd order UW (SOU) for the diffusive and convective and Rhiechow for velocity/pressure coupling (collocated grid), in a fractional step manner. Since I tested this with Ghia I believe they are properly implemented Can someone shade a light on this. I suspect I am stuffed with implementing the BC. For instance do we need to explicitly specify a BC for the corners. Normally, I don not set separate BC for the corners, since as the grid get refined the singularity from the corner fades away. With best regards, taw 
any suggestion from those online now
apology for the urgency; can some one suggest an explanation.

Hi,
I think I figured out the problem. The continuity equation (cell face velocities) bc was the problem. I should have set one extra grid line to zero for vf_i, unlike the centre velocities bc, since the computational molecule with Rhiechow is large. Or one sided differencing should have been implemted for the boundaries. One more correction a_i^j=transpose(cofactor(ja_i^j)). Regards, TAW 
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